1. Chronic hepatitis B virus and liver fibrosis: A mathematical model
Avner Friedman Ohio State University MBI
and
Nourridine Siwie University of Tennessee, NIMBioS

2. Hapatitis B Virus
Hepatitis B virus (HBV) is a viral infection that results in liver cirrhosis (a late stage of fibrosis), causing the destruction of the liver
Chronic HBV affects 350 million people worldwide, with 600,000 deaths annually
The disease is 50 time more infectious than HIV
Infection occurs by contact with infected persons (sexual contact, sharing needles, toothbrush, nail clippers, razors, etc.)
The symptoms do not show up immediately after infection: the delay time make take weeks, months, or even years
Vaccination is effective 90%

3. Diameter 42 nm, ~3000 nucleotides the long strand, and ~2000 nucleotides the short strand

4. drugs Adefovir ----decreases viral load in the liver
IFN- alpha -----decreases viremia (viral concentration in the blood) and inflammation
Our aim
Our aim is to develop a mathematical model to be used to evaluate the efficacy in combination therapy in terms of optimal proportions between the two agents, and optimal scheduling;
The objective functions to be minimized are the scar density, and the viral load.

7. Model equations
macrophages

8. macrophages
hepatocytes

9. T cells
Fibroblasts and myofibroblasts

10. ECM
scar

15. Intracellular virus

16. Extracellular virus

18. Parameters

22. Control case---no drugs

23. PDEs vs ODEs ---------------

27. Efficacy---- for scar (S) and for intracellular viral load (Vi)
The decrease in viral load by each of the drugs alone are in agreement with clinical results
Definitions
Efficacy---- for scar (S) and for intracellular viral load (Vi)

29. Synergy between the two drugs

31. Biological explanation of the synergy map

32. Conclusions
1. We have determined the proportion between the two drugs for which the combined treatment has maximal synergy, based on simple choice of
2. But this special choice needs to be adjusted to take into consideration negative side effects; these side effects will have to be incorporated into the model
3. The model can be used to explore intermittent treatment vs. continuous treatment with total amount of the drugs